Birth Death Swap population in random environment and aggregation with two timescales

Sarah Kaakai and Nicole El Karoui

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 218-248

Abstract: This paper deals with the stochastic modeling of a class of heterogeneous population in random environment, structured by discrete subgroups, and called birth–death–swap. In addition to demographic events modifying the population size, swap events, i.e. moves between subgroups, occur in the population. Event intensities are random functionals of the population. In the first part, we show that the complexity of the problem is significantly reduced by modeling the jump measure of the population as a multivariate counting process. This process is defined as the solution of a stochastic differential system with random coefficients, driven by a multivariate Poisson random measure. The solution is obtained under weak assumptions, by the thinning of a strongly dominating point process generated by the same Poisson measure. This key construction relies on a general strong comparison result, of independent interest.

Keywords: Heterogeneous population dynamics; Random environment; Point processes; SDEs driven by Poisson measures; Averaging; Stable convergence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:162:y:2023:i:c:p:218-248

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DOI: 10.1016/j.spa.2023.04.017

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